Home
Class 12
MATHS
"If " int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3...

`"If " int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3)+2x)dx=f(x)+C, " then the value of " f(1)xxf(-1) " is"-.`

Text Solution

Verified by Experts

The correct Answer is:
1
`int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3)+2x)dx`
`=int underset(I)(underbrace(x^(2)))underset(II)(underbrace(e^(x^(3)+x^(2)-1)(3x^(2)+2x)))dx+int e^(x^(3)+x^(2)-1)2x dx`
`=x^(2)e^(x^(3)+x^(2)-1)-int 2xe^(x^(3)+x^(2)-1)dx+int e^(x^(3)+x^(2)-1) 2xdx`
`=x^(2)e^(x^(3)+x^(2)-1)+C`
`implies f(1)=e " and " f(-1)=(1)/(e)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|7 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2, " then the value of " f(-1) " is"-.

if int (3^((1)/(x)))/(x^(2)) dx = k (3^((1)/(x))) + c , then the value of k is

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

If int (3^(1/x))/(x^2) dx = k (3^(1/x)) + c , then the value of k is …………. .

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Evaluate int (2x^(3)-1)/(x^(4)+x)dx

"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+f''(2)+f'(3)+f'(4) equals